In navigation systems that include a MINS and one or more SIMUs, MINS navigation parameters have been used as references to improve the accuracy of SIMU-computed navigation parameters. FIGS. 1, 1A and 1B show such systems. In the double subscript notation used herein to describe these systems, the left subscript denotes the location (MINS or SIMU) where a parameter is valid. The right subscript denotes a system (MINS or SIMU) based on whose information the parameter is computed.
Definitions applicable herein are:                MINS means Master Inertial Navigation System        SIMU means Slave Inertial Measurement Unit        α (alpha) means wander angle        PMM is the position of MINS computed based on MINS data        PSM is the nominal position of SIMU computed based on MINS data. “Nominal” means: without considering high frequency relative motion between MINS and SIMU.        PSB is the best estimated position of SIMU, computed based on MINS and SIMU data        VMM is the velocity of MINS computed based on MINS data        IVMM is the integral of velocity of MINS computed based on MINS data        IVSM is the integral of nominal velocity of SIMU computed based on MINS data        IVSS is the integral of velocity of SIMU computed based on SIMU data        VSS is the velocity of SIMU computed based on SIMU data        VSB is the best estimated velocity of SIMU        WMM is the body angular rate of the MINS computed based on MINS data expressed in the navigation coordinate frame        WSS is the body angular rate of the SIMU computed based on SIMU data expressed in the navigation coordinate frame        IWMM is the integral of body rate of MINS computed based on MINS data expressed in the navigation coordinate frame        IWSS is the integral of body rate of SIMU computed based on SIMU data expressed in the navigation coordinate frame        TN Bm is the transformation matrix from MINS's body frame to navigation coordinate frame        TBmV is the transformation matrix from vehicle frame to MINS's body coordinate frame        HM is the vehicle heading computed by MINS        TNBs is the transformation matrix from SIMU's body coordinate frame to navigation coordinate frame        TBsV is the transformation matrix from vehicle frame to SIMU's body coordinate frame        HS is the vehicle heading computed by SIMU        Inertial Coordinate Frame—This is a system of three orthogonal axes that is fixed with respect to inertial space. The three axes have one axis directed along the mean rotational axis of the earth, a second axis defined in the mean equatorial plane of the earth and a third axis orthogonal to these two axes. The stars are fixed with respect to inertial space and so the Inertial Coordinate Frame is fixed with respect to the stars. One of the inertial frame axes in the mean equatorial plane of the earth can be selected to point relative to the stars. For example the direction of the star Aries is sometimes chosen.        Earth-Fixed Coordinate Frame—This is a system of three orthogonal axes that rotates with respect to the Inertial Coordinate Frame at the rate of rotation of the earth. The earth has a mean rotation about its polar axis that is also one of the axes of the Inertial Coordinate Frame. The polar axis of the Earth-Fixed Coordinate Frame is coincident with the polar axis of the Inertial Coordinate Frame. A second axis of the Earth-Fixed Coordinate Frame lies in the mean equatorial plane of the earth in the direction of the longitudinal meridian that passes through Greenwich, England. The third axis is orthogonal to these two axes and thereby lies in the mean equatorial plane of the earth.        Navigation Coordinate Frame—The navigation coordinate frame is a system of three orthogonal axes that is defined at the position of a navigation system. The Navigation Coordinate Frame has one axis coincident with what is called the “local vertical” that is defined as the direction of the gravity vector at the position of the navigation system. A second axis is defined in the “local level” plane that is orthogonal to the gravity vector. For example, this second axis can be chosen to point in the East direction. The third axis of the Navigation Coordinate Frame points in the North direction since it is orthogonal to the other two axes. The Navigation Coordinate Frame is translated in the East direction from the Earth-Fixed Coordinate Frame axis that resides in the mean equatorial plane of the earth in the Greenwich meridian by the longitude of the instantaneous position of the navigation system and translated in the North direction by the latitude of the instantaneous position of the navigation system.        Body Coordinate Frame—The Body Coordinate Frame is a system of three orthogonal axes that is defined with respect to the vehicle that carries the navigation system. For example, for an airplane, one axis is normally pointed in the direction of the nose of the airplane, a second axis is pointed in the direction of the right wing and a third axis is pointed in the direction orthogonal to these other two axes.        A navigation system may be installed on an aircraft such that axes of measurement of force by accelerometers, and angular change measured by gyros, are generally aligned with the body coordinate frame defined with respect to the vehicle. In these cases the orientation of the body coordinate frame with respect to the navigation coordinate frame can be defined by three angles of rotation. The first rotation can be about the local vertical of the navigation coordinate frame through an angle called heading of the vehicle. A second rotation can then be defined about the axis in the level plane displaced from the East direction. This second rotation angle is called pitch of the vehicle. A third rotation angle can be defined about the body frame axis pointed in the direction of the nose of the vehicle. This third rotation angle is called the roll of the vehicle.        Inertial Sensor Reference Coordinate Frame—The inertial sensor reference coordinate frame is an orthogonal set of axes defined by the sensing axes of the gyros and accelerometers. In most cases an accelerometer and gyro pair are mounted so that their sensing axes are nominally coincident and directed along an axis of the inertial sensor reference frame. Consequently the sensing axes for three such pairs will be directed along one of the axes of the inertial sensor reference frame. For current strapdown inertial systems, the installation of the inertial system in the vehicle is such that the inertial sensor reference frame is nominally coincident with the body coordinate frame of the vehicle. This assumption applies to the description of the transfer alignment mechanization below.        Alignment—Alignment is the process of determining the orientation of inertial instrument axes, gyros and accelerometers with respect to the Navigation Coordinate Frame. An example of this process comprises determining the orientation of a Body Coordinate Frame of a vehicle with respect to the East, North and vertical direction at the instantaneous position of a vehicle.        Transfer Alignment—Transfer alignment is a term used in the inertial navigation system field to define the process where the orientation of the inertial instrument axes of one inertial navigation system that has not been aligned, is aligned, using information from a second inertial navigation system that is aligned with respect to the Navigation Coordinate Frame. When the Transfer Alignment process is complete, the unaligned inertial navigation system knows the orientation of its gyros and accelerometers with respect to the Navigation Coordinate Frame and can perform the navigation function.        
FIG. 1 shows a known MINS/SIMU system, in which a SIMU computes SIMU position (PSS) and velocity (VSS) information. A MINS provides reference position (PSM) and velocity (VSM) to a Kalman filter, after correction/compensation for the nominal lever arm linkage between the MINS location and the SIMU location. The Kalman filter determines the differences between the SIMU position and velocity information, and the MINS reference position and velocity information, and provides corrections to SIMU position and velocity to improve SIMU's navigation accuracy.
Because reference velocity (VMM) can be noisy, FIG. 1A shows an alternative to the system of FIG. 1, using the integral of MINS velocity, IVMM, instead of VMM. FIG. 1B shows another alternative to the system of FIG. 1, where the Kalman filter observes the difference of heading, in addition to the difference of position and velocity, computed by SIMU and MINS, and provides corrections to the SIMU.